Browsing by Author "Turkmen, Ergul"

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On rings with one middle class of injectivity domains
(UNIV OSIJEK, DEPT MATHEMATICSUNIV OSIJEK, DEPT MATHEMATICS, TRG LJUDEVITA GAJA 6, OSIJEK HR-31000, CROATIA, 2022) Demirci, Yilmaz Mehmet; Alizade, Rafail; Turkmen, Burcu Nisanci; Turkmen, Ergul; 0000-0003-3802-4211; 0000-0003-4444-9136; AGÜ, Mühendislik Fakültesi, Mühendislik Bilimleri Bölümü; Demirci, Yilmaz Mehmet
A module M is said to be modest if the injectivity domain of M is the class of all crumbling modules. In this paper, we investigate the basic properties of modest modules. We provide characterizations of some classes of rings using modest modules. In particular, we show that a ring having the class of crumbling modules as the only right middle class of injectivity domains is either a right V-ring or right Noetherian; and a commutative ring with this property is regular. We also give criteria for a ring having the class of crumbling modules as the only right middle class of injectivity domains.
Rings with modules having a restricted injectivity domain
(SPRINGER INTERNATIONAL PUBLISHING AG, GEWERBESTRASSE 11, CHAM, CH-6330, SWITZERLAND, 2019) Demirci, Yilmaz Mehmet; Turkmen, Burcu Nisanci; Turkmen, Ergul; 0000-0003-3802-4211; AGÜ, Mühendislik Fakültesi, Mühendislik Bilimleri Bölümü
We introduce modules whose injectivity domains are contained in the class of modules with zero radical and call them working-class. This notion gives a generalization of poor modules that have minimal injectivity domain. Semisimple working-class modules always exist for arbitrary rings whereas their predecessors do not. We investigate the rings over which every module is either injective or working-class. Right weakly V-rings are examples of these rings. Moreover, we study the existence of working-class simple modules and show that if there is a projective working-class simple right module, then the ring is a right GV-ring.
RINGS WITH VARIATIONS OF FLAT COVERS
(HONAM MATHEMATICAL SOC, DEPT MATHEMATICS, COLL NATURAL SCIENCE, CHOSUN UNIV, 309, PILMUN-DAERO, DONG-GU, GWANGJU, 501-759, SOUTH KOREA, 2019) Demirci, Yilmaz Mehmet; Turkmen, Ergul; 0000-0003-3802-4211; AGÜ, Mühendislik Fakültesi, Mühendislik Bilimleri Bölümü
We introduce flat e-covers of modules and define e-perfect rings as a generalization of perfect rings. We prove that a ring is right perfect if and only if it is semilocal and right e-perfect which generalizes a result due to N. Ding and J. Chen. Moreover, in the light of the fact that a ring R is right perfect if and only if flat covers of any R-module are projective covers, we study on the rings over which flat covers of modules are (generalized) locally projective covers, and obtain some characterizations of (semi) perfect, A-perfect and B-perfect rings.
WSA-Supplements and Proper Classes
(MDPIST ALBAN-ANLAGE 66, CH-4052 BASEL, SWITZERLAND, 2022) Demirci, Yilmaz Mehmet; Turkmen, Ergul; 0000-0003-3802-4211; 0000-0002-7082-1176; AGÜ, Mühendislik Fakültesi, Mühendislik Bilimleri Bölümü; Demirci, Mehmet Yılmaz
In this paper, we introduce the concept of wsa-supplements and investigate the objects of the class of short exact sequences determined by wsa-supplement submodules, where a submodule U of a module M is called a wsa-supplement in M if there is a submodule V of M with U + V = M and U ∩ V is weakly semiartinian. We prove that a module M is weakly semiartinian if and only if every submodule of M is a wsa-supplement in M. We introduce CC-rings as a generalization of C-rings and show that a ring is a right CC-ring if and only if every singular right module has a crumbling submodule. The class of all short exact sequences determined by wsa-supplement submodules is shown to be a proper class which is both injectively and co-injectively generated. We investigate the homological objects of this proper class along with its relation to CC-rings.